Proofs with Matricies

  • Thread starter joedozzi
  • Start date
  • #1
20
0

Homework Statement


Homework Equations



Question 1.jpg



The Attempt at a Solution



-(y, x) = -(YX-XY)
= XY-YX

Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)

And prove it that way? I am just really confused
 

Answers and Replies

  • #2
35,633
7,502

Homework Statement


Homework Equations



View attachment 50857


The Attempt at a Solution



-(y, x) = -(YX-XY)
= XY-YX

Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)

And prove it that way? I am just really confused

What you have above would work, but your notation is awful! Try to use the notation as given in the problem. Also notice that uppercase letters represent matrices, and lowercase letters represent the entries in a matrix.

Assuming that matrices X and Y are in M, then [X, Y] = ?
Keep working with the expressions you get until you end up with -[Y, X].
 
  • #3
20
0
[X, Y]= YX- XY
Thus [Y, X]= XY- YX
then -[Y, X]= -(XY- YX)
then -[Y, X]= -XY +YX

Like that? So i don't have to use matricies with variables, just use X and Y to represent a matrix?
 
  • #4
35,633
7,502
[X, Y]= YX- XY
Thus [Y, X]= XY- YX
then -[Y, X]= -(XY- YX)
then -[Y, X]= -XY +YX

Like that? So i don't have to use matricies with variables, just use X and Y to represent a matrix?

This is easier to follow.

[X, Y] = XY - YX = -(YX - XY) = -[Y, X]

Can you say why each pair of successive equal expressions is valid?
 
  • #5
20
0
Properties of Matricies?
 
  • #6
20
0
And Thanks your honestly a huge help!
 
  • #7
35,633
7,502
Properties of Matricies?
That's pretty vague. Also, there are a number of steps. One reason doesn't fit them all.
 

Related Threads on Proofs with Matricies

  • Last Post
Replies
2
Views
3K
Replies
3
Views
3K
  • Last Post
Replies
13
Views
823
  • Last Post
Replies
1
Views
2K
Replies
3
Views
5K
  • Last Post
Replies
7
Views
20K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
14
Views
4K
Top